In the military, everything works of numbers. Recruiting is a good example of a binomial distribution. I'll use NC Army National Guard for an example.
The NCARNG must have a set number of enlistments every year and they get the requirement for the year during October.
This year the number is: 2000 (so n = 2000), the 2 out comes recruiters deal with are do they enlist or do they not enlist so we have a success if they enlist or a failure if they do not enlist (success or failure). This will give us a probability of success of 0.50 (p = .5).
Since everyone interviewed is a different person they are considered independent from each other.
The above distribution if looked at on a year to year base meets the requirements for a binomial distribution:
The requirements are listed below:
1. Each trial can have only two outcomes or outcomes that can be reduced to two outcomes. These outcomes can be considered as either success or failure.
2. There must be a fixed number of trials.
3. The outcomes of each trial must be independent of each other.
4. The probability of a success must remain the same for each trial.
Mean is given by n*p = 2000*0.5 = 1000
Standard deviation = sqrt(n*p*q) = sqrt(2000*0.5*0.5) ...
This solution uses the binomial distribution and calculates the mean and standard deviation of the trials. All steps are shown.